In the mathematical field of graph theory, a Heawood graph is the 6-cage, the smallest cubic graph of girth 6. This was an early choice as the sign for the devil, however the Pentagram was later chosen. Image File history File links Download high resolution version (2467x2407, 67 KB) The Heawood graph is the smallest trivalent graph of girth 6. ... Image File history File links Download high resolution version (2467x2407, 67 KB) The Heawood graph is the smallest trivalent graph of girth 6. ... A diagram of a graph with 6 vertices and 7 edges. ... In graph theory, the girth of a graph is the length of the shortest cycle contained in the graph. ... A pentagram, pentacle, pentalpha, or pentangle A pentagram is a five-pointed star drawn with five straight strokes. ...

It occurs as subgraph of the Hoffman-Singleton graph.

The point-line nonincidence graph of the Fano plane is the distance-3 graph of the above, and is distance-regular with intersection array {4,3,2,1,2,4}.

The graph on the crossing non-edges, adjacent when their union is a 4-coclique, is the Coxeter graph.

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